"We'll meet you in court," Brewer told CNN' when asked how she would respond if President Barack Obama's Department of Justice decided to challenge the law. "I have a pretty good record of winning in court."

The American Civil Liberties Union is currently leading a court challenge. Attorney General Eric Holder, who met with a delegation of police chiefs from Arizona and elsewhere this week to discuss the law, has yet to indicate whether the federal government would file a legal challenge.

Obama, who has called the law "misguided," will meet with Brewer at the White House on Thursday, a White House official told CNN. It will be the first one-on-one meeting between the two since Brewer approved the law in April.

The new immigration law, implemented last month, allows police officers to check the residency status of anyone who is being investigated for a crime or possible legal infraction if there is reasonable suspicion the person is an illegal resident. Critics, including Holder, have said the law will promote racial profiling.

But Brewer said Tuesday the law does not target an individual's specific race. She also made clear driver's licenses are not sufficient to prove citizenship.

"It wouldn't matter if you are Latino or Hispanic or Norwegian," she said. "If you didn't have proof of citizenship and the police officer had reasonable suspicion, he would ask and verify your citizenship. I mean, that's the way that it is. That's what the federal law says. And that's what the law in Arizona says."

Brewer strongly defended the law, saying she would not suspend it even if Obama sharply increased the number of U.S. troops at the Mexican border.

The Arizona governor also said the White House has not adequately communicated with her about Obama's recently announced plan to dispatch 1,200 National Guard troops to the border.

"I'm sitting here with no good information. It would be very helpful, I might say, if somebody would give me something in writing telling me what they're sending to Arizona, how will it be distributed?" she said.